How to prevent bolts from rusting and sticking in the toilet tank?

The best solution is to purchase a new set of bolts that are made of stainless steel or brass. Both will not rust the same way that a iron or steel bolt will. They will cost a little bit more but will pay back in the long term.

My experience has been that the brass bolts after years can sometimes build up their own kind of corrosion that can make it difficult to remove the nuts. This seems to be related to the water chemistry and to some degree if there is a micro leak by the bolt. Stainless steel bolts are the best in my experience and I have been very happy with the toilet repairs where I have used them.

Aside from using non-corroding bolts (which can be hard to track down in today's "make it cheap, even if it's useless" economy) applying silicone grease liberally can be helpful. If your local sources of supply only have rusty steel, be ready to find better ones online. Silicone grease (specifically) does not damage rubber seals - I'm particularly fond of vacuum grease (a little harder to find, but one tube has lasted me decades once found.)

Somewhere I have a set of steel bolts for a toilet tank. They, with rubber washers, were cheaper than rubber washers alone (or else there were no rubber washers alone, I can't recall now.) I did not use those bolts, as the bolts on the toilet were brass and far better than the new ones, 40 years on - just the rubber had deteriorated. I did also grease them up. Grease in general is strongly hydrophobic, and vacuum grease in particular is thick enough to act as a secondary seal against leaks (it does not move much, and will fill any irregularities.)

I had this same problem several years ago on my 25 yr old house. I recently saw the commercial for flex seal paint spray. They only had the black color but now I would prefer the white. After 2 years it still looks ok.